In recent years, velocity and temperature transformations have received increasing attention in the study of compressible wall-bounded turbulent flows (Trettel et al., 2016; Huang et al., 2023; Xu et al., 2025). The goal of these transformations is to map the compressible velocity and temperature profiles onto their incompressible counterparts, thereby recovering the compressible law of the wall. Building upon these findings, we propose a flux-controlled wall model (FCWM) for Large Eddy Simulation (LES). Unlike conventional wall-stress models that solve the turbulent boundary layer equations, FCWM formulates near-wall modeling as a control problem applied directly to the outer LES solution. It consists of three components: (1) the compressible law of the wall, (2) a feedback flux-control strategy, and (3) a shifted boundary condition. Inspired by previous studies (Nicoud et al., 2001; Bae et al., 2022), FCWM adjusts the wall shear stress and heat flux based on discrepancies between the computed and target transformed velocity and temperature profiles. To evaluate the proposed wall model, LES of compressible turbulent channel flows were performed over a broad range of Mach and Reynolds numbers Mb = 0.74–4.0, Reb = 7667–34000. The wall-modelled LES reproduces mean velocity and temperature profiles in good agreement with direct numerical simulation data. For all tested cases with Mb < 3, the wall model achieves relative errors below 4.1% , 2.7%, and 2.7% in friction coefficient, non-dimensional heat flux, and centerline temperature, respectively. Compared with the conventional equilibrium wall model, the proposed FCWM achieves higher accuracy in compressible turbulent channel flows without solving the boundary layer equations, thereby reducing computational cost.